Heat Equation

Question

Im trying to determine if a coin is real gold or if it is pyrite. The mass of the coin is 55.5 g. I heat the gold in a pot of boiling water, bringing it up to a temperature of 100.0 celsius. I then add the metal to 200.0 g of water at 22.0 celsius. The water warms to a final temperature of 22.7 celsius. Is the coin gold or pyrite? (S gold = 0.129 J/g.celsius; S pyrite = 0.518 J/g.celsius)

Answer 1

Hello Anna

 

To solve this question, we first need to calculate how much heat was absorbed by the water.  The heat absorbed by the water will equal the heat lost by the metal as per the Law of Conservation of Energy.  We then use this value of heat lost by the metal to determine its specific heat capacity, which will then tell us whether the coin is gold or pyrite.

 

a) Heat absorbed by water

 

q_water = c_water x m_water x ΔT

 

c_water = 4.184 J / gºC  (specific heat capacity of water)

 

mass of water = 200.0 g

 

T_i = 22.0 ºC

 

T_f = 22.7 ºC

 

ΔT = T_f - T_i

 

q = c_w x m_w x ΔT =  4.184 J / gºC x 200.0 g x (22.7 - 22.0 ºC)

 

   = + 585 J  (sign for q is positive since heat was absorbed)

 

b)  q absorbed by water = q lost by the metal

 

+ 585 J = - 585 J  (q is negative for the metal since it lost heat)

 

c)  solve for specific heat capacity of the metal

 

mass of metal = 55.5 g

T_i = 100.0 ºC

T_f = 22.7 ºC

 

c_metal = q_metal / (m_metal x ΔT_metal)

 

      = - 585 J / (55.5 g x (22.7 - 100.0 ºC))

 

      = - 585 J / - 4290 g ºC

 

      = 0.136 J/gºC

 

The closest value the specific heat matches to is gold (0.129 J/gºC).